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A Virtual Master’s Degree Program for Secondary Mathematics Teachers PowerPoint Presentation

A Virtual Master’s Degree Program for Secondary Mathematics Teachers

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### A Virtual Master’s Degree Program for Secondary Mathematics Teachers

Presented by Ozlem Korkmaz, University of Wyoming

8TH Annual Math & Science Teacher’s Conference at Casper College, 2010

Distance Education around the world Mathematics Teachers

United States of America Mathematics Teachers

Description of the Program Mathematics Teachers

- The virtual master’s degree program, offered jointly by the University of Northern Colorado and the University of Wyoming, started in the summer of 2009 for secondary mathematics teachers to improve mathematics achievement in secondary education in the Rocky Mountain region.

Vision Mathematics Teachers

- Increase student understanding of mathematics by promoting a master’s degree program for 7-12 grade mathematics teachers, which aims at developing highly qualified, culturally competent, and pedagogically effective mathematics teachers
in Colorado and Wyoming.

Why virtual? Mathematics Teachers

- The Rocky Mountain region is a vast, sparsely populated, and rural region where teachers lack access to professional development programs (PD).
- In-service teachers are not able to leave their positions to attend PD.
- The number of faculty to provide PD in such a vast region is limited.
- By means of alternative delivery formats, we make the master’s degree accessible to teachers in their home region.

Why important? Mathematics Teachers

- Online teacher professional development programs are gaining an important place in higher education as a means to enhance students’ achievement in schools
- Online professional development programs (OPD) for teachers are also increasing as the rapid development of technology allows distance education to grow.
- Virtual or online degree programs provide teachers with flexibility without the constraints of geographical borders or time.

Goals for Math TLC Mathematics Teachers

The goals of the master’s program Mathematics Teachers

Develop a shared vision of mathematics as a culturally rich subject in which K-12 mathematics proficiency is defined by shared community standards

Mathematics as a culturally rich subject subject in which K-12 mathematics proficiency is defined by shared community standards

- Mathematics is constructed within a cultural context.
- Stigler (1989) says, “Mathematics itself consists not only symbolic technologies but also of other cultural products-such as values, beliefs, and attitudes […] Educators should teach the values of mathematical culture, not because it will help children learn mathematics, but because values are part of the mathematics that children should learn.” (p. 369).

Mathematics as a culturally rich subject subject in which K-12 mathematics proficiency is defined by shared community standards

- In ancient times, in Egypt, farmers along the Nile river needed Geometry. The Nile would flood the land and destroy the farm areas each year. When the waters receded, the boundaries had to be redefined by measuring fields.
- The Egyptians (about 1800 BC) had accurately determined the volume of the frustum of a square pyramid.

MCRS (Cont’…) subject in which K-12 mathematics proficiency is defined by shared community standards

- Babylonians’ (2000-1600 BC) geometry was empirical, and limited to those properties physically observable. Through measurements they approximated the ratio of the circumference of a circle to its diameter to be 3.
- The Maya number system was a base twenty system. One of the Maya’s calendar, Tzolkin, composed of 260 days, 13 months of 20 days.

Develop teachers’ knowledge, skills and disposition to effectively teach mathematics in a culturally diverse classroom

What is Culturally Responsive Teaching (CRT)? effectively teach mathematics in a culturally diverse classroom

Culturally Responsive Teaching (CRT) effectively teach mathematics in a culturally diverse classroom

Gay (2000) defines culturally responsive teaching as using the cultural knowledge, prior experiences, and performance styles of diverse students to make learning more appropriate and effective for them; it teaches to and through the strengths of these students.

A learning experience drawn from a legend of Maori people in New Zealand

In the South Island [of New Zealand] there is a lake whose waters, by day and by night, rise and fall. The Maori people know that the pulsing of the water comes from the beating of a giant’s heart, the heart of Matau who was burnt by the brave Matakauri. The waters of Lake Wakatipu rise and fall about every five minutes. If the lake was formed about 1000 years ago, how many times has Matau’s heart beat since then? If Matau’s heart beat once every three minutes, how many times would Lake Wakapitu have risen and fallen over the last 100 years? (Heays, Copson, & Mahon, 1994, p.8 as cited by Averill, Anderson, Easton, Te Maro, Smith, and Hynds (2009).)

Literature suggests New Zealand

- Developing a knowledge base about cultural diversity
- Learning mathematical content from ethnically and culturally diverse origins
- Participating in and building a caring community of learners-this includes developing ways to calibrate teacher intentions with student perceptions.

Literature suggests (Cont’…) New Zealand

- Seeing personal communication patterns and using that awareness to learn to communicate effectively with diverse students.
- Responding supportively to socio-economic, cultural, and ethnic diversity in the delivery of instruction.

Characteristics described by Gay (2000) New Zealand

- It acknowledges the legitimacy of the cultural heritages of different ethnic groups, both as legacies that affect students' dispositions, attitudes, and approaches to learning and as worthy content to be taught in the formal curriculum.
- It builds bridges of meaningfulness between home and school experiences as well as between academic abstractions and lived sociocultural realities.
- It uses a wide variety of instructional strategies that are connected to different learning styles.
- It teaches students to know and praise their own and each others' cultural heritages.
- It incorporates multicultural information, resources, and materials in all the subjects and skills routinely taught in schools

Some of the Principals of CRT New Zealand

There are consistent messages, from both the teacher and the whole school, that students will succeed, based upon genuine respect for students and belief in student capability.

There are consistent messages, from both the teacher and the whole school, that students will succeed, based upon genuine respect for students and belief in student capability.

Communication of High Expectations

Principals of CRT New Zealand

There are consistent messages, from both the teacher and the whole school, that students will succeed, based upon genuine respect for students and belief in student capability.

Instruction is designed to promote student engagement by requiring that students play an active role in crafting curriculum and developing learning activities.

Active Teaching Methods

Principals of CRT New Zealand There are consistent messages, from both the teacher and the whole school, that students will succeed, based upon genuine respect for students and belief in student capability.

Within an active teaching environment, the teacher's role is one of guide, mediator, and knowledgeable consultant, as well as instructor.

Teacher as facilitator

Principals of CRT New Zealand There are consistent messages, from both the teacher and the whole school, that students will succeed, based upon genuine respect for students and belief in student capability.

There is an ongoing participation in dialogue with students, parents, and community members on issues important to them, along with the inclusion of these individuals and issues in classroom curriculum and activities.

Inclusion of Culturally and Linguistically Diverse Students

Principals of CRT New Zealand There are consistent messages, from both the teacher and the whole school, that students will succeed, based upon genuine respect for students and belief in student capability.

To maximize learning opportunities, teachers gain knowledge of the cultures represented in their classrooms and translate this knowledge into instructional practice.

Cultural Sensitivity

Extend teachers’ content knowledge beyond the content they customarily teach to students

Polygons on earth customarily teach to students

Regular Hexagon in chemistry customarily teach to students

Snow flakes- Regular Hexagon customarily teach to students

Honey comb-Regular Hexagon customarily teach to students

For n-sided polygon customarily teach to students

- Find the number of diagonals passing by one vertex
- Find the formula that determines the number of diagonals.
- Determine the number of triangles formed by drawing all diagonals passing through one vertex
- What is the total sum of the measure of the interior angles?
- What is the total sum of the measure of the exterior angles?

Definition customarily teach to students

- Let where be a set of points in the plane such that .
- The union of the line segments is an n-sided polygon whose vertices are
and whose edges are the line segments .

A student might ask… customarily teach to students

- Although the definition admit ,
what if n=1, n=2? How can it be called and represented?

Response… customarily teach to students

In spherical geometry, it is possible to have a two sided polygon, namely digon

Spherical triangle customarily teach to students

Euclid’s Postulates on the Sphere customarily teach to students

- Postulate 1: Two points determine a unique line
- Is this postulate valid in spherical geometry?

Spherical Geometry Terms customarily teach to students

- Polar points are the end points of the sphere’s diameter (called as antipodal)
- Straight lines are great circles; that is circles that contain any pair of polar points.
- A segment (arc segment) on a sphere is the shortest distance between two points.
- A segment is always part of a great circle, and is also called geodesic.

Response to the question customarily teach to students

- If two points are antipodal, then there are an infinite number of straight lines containing these two points, such as all the lines of longitude. Euclid’s first postulate is therefore not valid in spherical geometry.

Euclid’s parallel postulate customarily teach to students

- Given a line L and a point P not on L, there exists a unique line though P parallel to L.
- How would you re-word this postulate so that it is true for spherical geometry?
- Given a line G and a point P not on G, every line through P intersects G; that is, no line through P is parallel to G.

Engage teachers in actively building their pedagogical content knowledge (Shulman, 1987), enabling them to enlarge their repertoire of pedagogical methods, skills and knowledge congruent with standards (NCTM, 2000; CDE, 2007; WDE, 2003).

Cone Project content knowledge (Shulman, 1987), enabling them to enlarge their repertoire of pedagogical methods, skills and knowledge congruent with standards (NCTM, 2000; CDE, 2007;

- Teacher participants explored geometry on the cone in groups of three.
- Teacher participants explored what interested them, wrote a report, and presented their findings to their classmates.
- Engaging in such a project will enable them to apply the same pedagogy in their practice.

Empower participants as lifelong professional learners who regularly reflect on themselves, students, and community context to improve teacher practice and student learning

Action Research Project (ARP) regularly reflect on themselves, students, and community context to improve teacher practice and student learning

Reflection

Planning

Action

Data Collection

Data Interpretation

ARP Example regularly reflect on themselves, students, and community context to improve teacher practice and student learning

Courses & Curricula regularly reflect on themselves, students, and community context to improve teacher practice and student learning

- The Math TLC provides 30- credit hour, 2-year master’s program, which involves face-to-face and online courses.
- Of 30 credits, 18 hours mathematics and 12 hours are mathematics education courses.
- All courses address NCTM principals and standards: teachers experience as learners the kinds of instruction recommended for K-12 students.

Mathematics Courses regularly reflect on themselves, students, and community context to improve teacher practice and student learning

Mathematics Education Courses regularly reflect on themselves, students, and community context to improve teacher practice and student learning

Research-based course design characteristics regularly reflect on themselves, students, and community context to improve teacher practice and student learning

- Employ a research-based instructional design, modeling learning strategies that promote effective classroom learning and teaching, and that teachers can also use with their students. (Bybee, 2006)
- Build new knowledge upon teachers’ prior knowledge.
- Support learning through interaction among teachers about mathematical ideas

Research-based course design characteristics (Cont’…) regularly reflect on themselves, students, and community context to improve teacher practice and student learning

- Convey clear purpose and outcomes. (NRC, 1999, 2005).
- Incorporate a variety of learning activities to engage teachers, appeal to different learning styles, and explore the cultural capital of teachers and the students they teach (Bourdieu, 1986; Civil, 2002; Kuhn, 2005; NRC, 2000).
- Assess teacher understanding frequently.

Research-based course design characteristics (Cont’…) regularly reflect on themselves, students, and community context to improve teacher practice and student learning

- Situate learning within meaningful, relevant contexts (e.g., action research; Nentwig & Waddington, 2005).
- Cultivate a safe, non-threatening, low-risk environmentfor teachers to express new ideas and try out new approaches, such as incorporating collaborative learning strategies within course designs.

Questions?? regularly reflect on themselves, students, and community context to improve teacher practice and student learning

References regularly reflect on themselves, students, and community context to improve teacher practice and student learning

- Averill, Anderson, Easton, Maro, Smith, & Hynds (2009). Culturally responsive teaching of mathematics: Three models from linked studies. Journal for Research in Mathematics Education, 40(2), 157-186.
- Bishop, A. J. (1988). Mathematics education in its cultural context. Educational Studies in Mathematics, 19(2), 179-191. Retrieved from http://www.jstor.org/stable/3482573?seq=2
- Bishop, A. (1991). Mathematical enculturation: A cultural perspective on mathematics education. Dordrecht: Kluwer
- Ross, S. W., (2000). Non-Euclidean Geometry. Retrieved from http://library.umaine.edu/theses/pdf/RossSW2000.pdf
- Stigler, J. W. (1989). Review: Mathematics meets culture. Journal for Research in Mathematics Education. 20(4), 367-370. Retrieved from http://www.jstor.org/stable/pdfplus/749442.pdf
- http://www.intime.uni.edu/multiculture/curriculum/culture/Teaching.htm

THANK YOU regularly reflect on themselves, students, and community context to improve teacher practice and student learning

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